Method for implementing a resonator under electrostatic forces

ABSTRACT

In an implementation in rate gyro mode, the method comprises the steps of exciting the vibrating member by means of a combination of control signals comprising an amplitude control signal at the resonant frequency of the vibrating member or at a frequency twice the resonant frequency, a precession control signal at a frequency twice the resonant frequency, and a quadrature control signal at DC, at the resonant frequency, or at a frequency twice the resonant frequency. In free gyro mode, the method includes the steps of applying a combination of signals to common electrodes  5  and of applying said combination in alternation to main electrodes  5.1  and  5.2  and to secondary electrodes  7.1  and  7.2  interleaved between the main electrodes.

[0001] The present invention relates to a method of implementing anelectrostatic resonator for use as an inertial rotation sensor.

BACKGROUND OF THE INVENTION

[0002] Electrostatic resonators are known, in particular from documentsEP-A-0 810 418 or FR-A-2 792 722, comprising a vibrating member in theform of a metallized bell adapted to be set into vibration at a resonantfrequency under the effect of electrostatic forces generated byelectrodes disposed facing a portion of the vibrating member.

[0003] The resonator is adapted to operate in rate gyro mode or in freegyro mode. In rate gyro mode, the vibrating member is excited by meansof a combination of control signals applied at the resonant frequency ofthe vibrating member and modulated to generate an amplitude controlsignal, a precession control signal, and a quadrature control signal,these control signals being applied in such a manner that measuring thevibration of the vibrating member and demodulating said vibration at theresonant frequency of the vibrating member enable the speed of rotationto which the resonator is being subjected to be determined by making useof appropriate equations.

[0004] The accuracy with which the speed of rotation is calculated isnaturally a function of the accuracy with which the various terms of theequation giving the speed of rotation to be measured are themselvesdetermined. One of these terms is the amplitude of the vibrationobtained by applying amplitude control. It is this term which is knownwith the least accuracy and stability. Furthermore, quadrature controlis applied in the same directions as precession control, and when thequadrature control and the precession control are both applied in theform of a signal modulated at the resonant frequency, any phase error inimplementing quadrature control becomes projected onto precessioncontrol and gives rise to resonator drift error.

[0005] The same problems arise when the resonator is used in free gyromode, i.e. when the vibrating member is excited by means of acombination of control signals comprising only an amplitude controlsignal and a quadrature control signal.

[0006] It is also known from document U.S. Pat. No. 5,850,041 to controla resonator in free gyro mode by applying the amplitude control at twicethe resonant frequency and by applying quadrature control in the form ofa DC voltage. However, according to that document, quadrature control isapplied separately from amplitude control over a very large number ofseparate electrodes, i.e. sixteen or even thirty-two separateelectrodes. The resonator is thus itself extremely expensive to make,not only because of the difficulty of making a large number ofelectrodes accurately, but also because of the difficulty of makingconnections between all of those electrodes and an external processor.In addition, the associated control circuit is very complex and thusalso very expensive.

OBJECT OF THE INVENTION

[0007] An object of the invention is to provide a method of implementingan electrostatic vibrating resonator operating with great accuracy,preferably while using a small number of electrodes and connections tosaid electrodes.

BRIEF DESCRIPTION OF THE INVENTION

[0008] In a first aspect, the invention provides a method ofimplementing a resonator in rate gyro mode, the resonator comprising avibrating member adapted to be set into vibration at a resonantfrequency under the effect of electrostatic forces generated byelectrodes placed facing a portion of the vibrating member, the methodcomprising the steps of exciting the vibrating member by means of acombination of control signals comprising an amplitude control signal, aprecession control signal, and an amplitude-modulated quadrature controlsignal, of measuring vibration of the vibrating member, and ofdemodulating the vibration at the resonant frequency of the vibratingmember, the precession control signal being applied at a frequency thatis twice the resonant frequency. Thus, cross-modulation occurs betweenthe precession signal and variation in the airgaps facing the controlelectrodes, such that by converting double argument trigonometricformulae present in the terms that result from excitation at doublefrequency into single argument trigonometric formulae, and byeliminating terms of negligible value that result from this calculation,and equation is obtained in which the terms which include the amplitudeof the vibration are eliminated. Vibration amplitude thus has noinfluence on calculating speed of rotation. The accuracy with which thespeed of rotation of the resonator is determined in thus increased.

[0009] In an advantageous implementation in rate gyro mode and in whicha basic implementation in free gyro mode for which the precessioncontrol signal is eliminated, the amplitude control signal is applied ata frequency twice the resonant frequency during a stage of sustainingthe vibration of the vibrating member. Thus, in both cases, equationsgiving the speed of rotation of the resonator are simplified so that theelectronics for controlling and determining the speed of rotation of theresonator can be simplified while still enabling the required accuracyto be obtained.

[0010] In a second aspect of the invention, the quadrature controlsignal is applied in the form of a DC signal to electrodes that arecommon with the electrode control signal. Thus, any phase error relativeto precession control or any orientation error in the amplitude controlis eliminated while minimizing the number of electrodes needed forimplementation. In this implementation, the electrostatic forcesresulting from quadrature control are the consequence ofcross-modulation that result from variation in the airgaps facing theelectrodes. In order to maximize this airgap variation, the amplitudecontrol signal is preferably applied in such a manner that the vibrationof the vibrating member is oriented so that a vibration node is inregister with a gap between two electrodes. The portion of the vibratingmember in register with an electrode is then subjected to non-zeroairgap variation which makes it possible to obtain strongcross-modulation and consequently better measurement accuracy.

[0011] In yet another aspect of the invention associated with theresonator being implemented in free gyro mode, the amplitude control ata frequency double the resonant frequency is applied to the vibratingmember itself, and the quadrature control is applied to electrodes whichserve simultaneously for detection. This achieves an increased dynamicrange, thereby improving measurement accuracy with a minimum number ofconnections.

BRIEF DESCRIPTION OF THE DRAWING

[0012] Other characteristics and advantages of the invention appear onreading the following description of a method of implementing avibrating hemispherical resonator given with reference to theaccompanying figures, in which:

[0013]FIG. 1 is an axial section view on line I-I of FIG. 2; and

[0014]FIG. 2 is a plan view of the electrodes of the resonator which isshown in section on line II-II of FIG. 1.

DETAILED DESCRIPTION OF THE INVENTION

[0015] For a better understanding of the invention, the resonator isshown on a greatly enlarged scale with the thicknesses of the electrodesand the airgaps being exaggerated.

[0016] In the embodiment shown, the resonator comprises in conventionalmanner a hemispherical vibrating member 1, e.g. a bell made of silicaand fixed by a rod 4 to a base 3. The inside surface of the bell 1 andits edge and also the rod 4 are covered in a layer of metal 2. The base3 carries main electrodes given overall numerical reference 5 andindividual references 5.1, 5.2, . . . , 5.8 enabling them to beidentified individually. The electrodes 5 extend facing the edge of thevibrating member 1.

[0017] In the embodiment shown, the resonator also has a shieldelectrode given overall reference 6, which electrode is subdivided intotwo portions 6.1 and 6.2 each comprising four auxiliary electrodes givenoverall numerical reference 7 and particular numerical references 7.1for the auxiliary electrodes of the portion 6.1 and 7.2 for theauxiliary electrodes of the portion 6.2. The electrodes 7.1 and 7.2extend in alternation between the electrodes 5. The portion 6.1 of theshield electrode is constituted by a central disk from which theauxiliary electrodes 7.1 extend radially outwards, while the portion 6.2of the shield electrodes is constituted by a circular ring extendingaround the electrodes 5 and from which the auxiliary electrodes 7.2extend radially inwards.

[0018] In order to implement rate gyro mode, and in the preferredimplementation, the vibrating member is initially set into vibration byapplying an amplitude control signal CA. The vibrating member 1 cannotbe set into vibration by means of a signal at twice its resonantfrequency. While it is being set into vibration, the amplitude controlsignal is thus applied at the resonant frequency. Preferably, theamplitude control signal is applied so that vibration of the vibratingmember is oriented in such a manner that a vibration node is in registerwith a gap between two electrodes. For this purpose, the amplitudecontrol signal CA is applied modally in quadrature to at least twoelectrodes. In the embodiment shown which operates in mode 2, theamplitude control signal CA is applied in phase to at least twoelectrodes that are at 45° to each other, e.g. to the electrodes 5.1 and5.2. The resulting vibration then presents an antinode in register withthe gap between the electrodes 5.1 and 5.2 as represented by a bolddouble-headed arrow in the figure. Corresponding antinodes appear in thegaps between the electrodes 5.3 & 5.4, 5.5 & 5.6, and 5.7 & 5.8.Simultaneously, nodes are formed in the gaps between electrodes 5.2 &5.3, 5.4 & 5.5, 5.6 & 5.7, and 5.8 & 5.1, as represented by small boldcircles in FIG. 2. To increase the speed at which vibration isestablished, diametrically opposite electrodes, i.e. electrodes 5.2 and5.6 in the above-described example are also fed with the same amplitudecontrol signal. The vibration oriented in this way thus has non-zeroamplitude in register with each main electrode 5.

[0019] The same vibration position can also be obtained by feeding theelectrode 5.2 or the electrodes 5.2 and 5.6 with a signal CA, and theelectrode 5.3 or the electrodes 5.3 and 5.7 with a signal −CA (i.e. inphase opposition).

[0020] In applications where control is performed in alternation withdetection by time division multiplexing of control and detection, thespeed of setting into vibration can also be increased by powering alleight main electrodes 5 simultaneously. For a vibration position asshown in FIG. 2, the electrodes 5.1, 5.2, 5.5, and 5.6 are fed in thiscase with a signal CA while the electrodes 5.3, 5.4, 5.7, and 5.8 arefed with a signal −CA.

[0021] In a preferred implementation, after the stage of setting intovibration, amplitude control is switched to a sustaining stage in whichthe amplitude control signal CA is applied at a frequency which isdouble the resonant frequency. The control signal can then be appliedeither to the electrodes 5 or to the metallized layer 2 of the bell 1.At this frequency, variation in the airgap in register with theelectrodes suffices to generate electrostatic forces that sustainvibration, even when the same control signal is applied to all of theelectrodes 5 or when a single amplitude control signal is applied to thebell.

[0022] After the stage of putting the resonator into vibration,precession control is applied to maintain the orientation of thevibration in spite of movements of the equipment on which the resonatoris mounted. According to the invention, this precession control CP, ofamplitude which is calculated in conventional manner, is applied at afrequency which is twice the resonant frequency to the controlelectrodes with appropriate sign for keeping vibration in a stableorientation.

[0023] In parallel, quadrature control CQ is preferably applied inaccordance with the invention as a DC signal of amplitude calculated inconventional manner for canceling resonator drift. As for precessioncontrol, quadrature control is applied appropriately as a function ofwhich electrodes are used for applying this control.

[0024] By way of example, when the sustaining amplitude control signalis applied at the frequency which is twice the resonant frequency, asignal CA−CP−CQ is applied to electrode 5.1 while a signal CA+CP+CQ isapplied to the electrode 5.2 As before, the speed of response can beincreased by applying the same signals respectively to electrodes 5.5and 5.6. When using eight electrodes, the signal CA−CP−CQ is applied tothe electrodes 5.1, 5.3, 5.5, and 5.7, while the signal CA+CP+CQ isapplied simultaneously to the electrodes 5.2, 5.4, 5.6, and 5.8. Whenthe amplitude control signal CA is applied to the bell, this componentis eliminated from the signals applied to the control electrodes.

[0025] When implemented in rate gyro mode, the two portions 6.1 and 6.2of the shield electrode are connected to ground so as to perform theusual function of reducing cross-talk between electrodes.

[0026] When only four electrodes are used for applying control signals,the other electrodes are available for detecting the modified vibrationin order to calculate precession control and the speed of rotation ofthe resonator. A single electrode may be used for such reception.Nevertheless, for a better dynamic range, at least two electrodes andpreferably four electrodes are used for reception.

[0027] In the example described above where the control signals areapplied to the electrodes 5.1, 5.2, 5.5, and 5.6, the signal detected onthe electrode 5.3 is designated D5.3, the signal detected on theelectrode 5.4 is designated D5.4, . . . , and vibration amplitude can bemeasured by any one of the combinations D5.3+D5.4, D5.3+D5.7, D5.4+D5.8,D5.3+D5.8, D5.4+D5.7, or indeed D5.3+D5.4+D5.7+D5.8. When usingmultiplexing to alternate control and detection, amplitude measurementcan be performed on all eight electrodes 5 by the combinationD5.1+D5.2+D5.5+D5.6−D5.3−D5.4−D5.7−D5.8. Servo-control error can bemeasured by any one of the following combinations: D5.3−D5.4, D5.3−D5.8,D5.7−D5.4, or D5.3−D5.4+D5.7−D5.8.

[0028] In an application in free gyro mode, precession control iseliminated but the resonator may otherwise be implemented in the samemanner as in rate gyro mode. Nevertheless, when implementing free gyromode, the orientation of vibration is no longer fixed and is a functionof the movements to which the resonator is subjected. In particular, thepositions of the nodes vary as a function of the movement of theresonator such that at certain instants, the position of a node willcoincide with the center of an electrode, and when using a DC quadraturecontrol signal, this signal is no longer subjected to cross-modulationbecause there is no variation of airgap. In another aspect of theinvention, the shield electrode is used to apply the quadrature controlto electrodes which are not in register with a vibration node.

[0029] To describe this implementation, the starting situation is thatin which the main electrodes used are the electrodes 5.1, 5.2, 5.5, and5.6. While sustaining vibration and in the absence of any movement ofthe resonator, the signal CA−CQ is applied to the electrodes 5.1 and 5.5while the signal CA+CQ is applied to the electrodes 5.2 and 5.6.Assuming that the resonator is subjected to movement causing thevibration to turn clockwise, then the node which was initially betweenthe electrodes 5.2 and 5.3 moves until this node comes close to themiddle of the electrode 5.2. In this situation, the quadrature controlapplied to the electrode 5.2 ceases to effective. In order to avoid thisloss of effectiveness, the signal CA−CQ is switched to the portion 6.1of the shield electrode and the signal CA+CQ to the portion 6.2 of theshield electrode. The node which is in register with the electrode 5.2is then halfway between the electrodes 7.1 and 7.2 which are subjectedrespectively to the signals CA−CA and CA+CQ. The airgap in register withthe electrodes 7.1 and 7.2 is thus varying so that quadrature control issubjected to cross-modulation. Quadrature control is thus again fullyeffective. The control signals are thus applied in alternation to themain electrodes 5 and to the secondary electrodes 7 as vibration turnsso as to keep the vibration nodes between the electrodes to which thequadrature control signal is applied. In this context, it should beobserved that in order to switch over the control signals from one groupof electrodes to the other, it suffices to bring the amplitude of thecontrol signal on the inactive electrodes to zero without it beingnecessary to switch the control signal from one group of electrodes tothe other. The method can thus be used in space where it is not possibleto use electronic switches.

[0030] As explained above, increasing the number of electrodes to whichthe control signals are applied makes it possible to increase thedynamic range and thus the accuracy of operation. In addition, inresonators used in space, it is not possible to perform switching of theelectrodes between a control function and a detection function. Forimplementation in space it is therefore usually necessary to allocatehalf of the main electrodes to control and the other half to detection.

[0031] In a preferred implementation of the invention in free gyro mode,it is nevertheless possible to allocate the same electrodes both tocontrol and to detection.

[0032] In this implementation, during the stage of sustaining vibration,the amplitude control signal is applied to the bell at a frequency twicethe resonant frequency. The DC quadrature control signal −CQ is appliedto the main electrodes 5.1, 5.3, 5.5, and 5.7 while the DC quadraturecontrol signal CQ is applied to the main electrodes 5.2, 5.4, 5.6, and5.8.

[0033] Simultaneously, each of the main and auxiliary electrodes isconnected to a detector member which, in conventional manner, is acharge amplifier, i.e. an operational amplifier including a capacitorconnected between the inverting input which is connected to an electrodeof the resonator and the output of the amplifier. Furthermore, thequadrature control signal is applied to the non-inverting input and isadded to the detection signal. Since the quadrature control signal is aknown DC voltage, it is easy to subtract this signal in order to obtainthe detection signal alone. In this respect, it should be observed thattwo diametrically opposite electrodes may be connected in parallel tothe same charge amplifier.

[0034] While the vibration is turning, quadrature control is appliedalternately to the main electrodes and to the auxiliary electrodes asdescribed above. With this implementation of the invention it sufficesto have eleven connections (the bell, the eight main electrodes, and thetwo portions of the shield electrode) in order to be able to apply thecontrol signal to eight electrodes and to pick up the detection signalon eight electrodes.

[0035] On this subject, in yet another aspect of the invention, it ispossible to calibrate the gain of the detectors so that it is the sameon two paths in quadrature. Vibration is analyzed at a frequency whichis twice the resonant frequency for electrodes that are modally inquadrature when a vibration node is in register therewith. Thiscalibration can be performed either during an initialization stage byapplying a precession control signal to place a vibration nodesuccessively in register with each of the electrodes, or by performingcalibration measurement each time it is detected that vibration is in aposition for which a vibration node is in register with an electrode. Byway of example, during an initialization stage, vibration is initiallyoriented so that a vibration node is in register with the electrodes5.2, 5.6, 5.4, and 5.8, the electrodes 5.2 and 5.6 being connected inparallel to a first charge amplifier having gain G1 while the electrodes5.4 and 5.8 are connected to a second charge amplifier having gain G2.By demodulating the vibration at a frequency twice the resonantfrequency, it is possible to determine the gains G1 and G2. Thevibration is then turned so that a vibration node comes into registerwith the electrodes 5.1, 5.3, 5.5, and 5.7. In the same way as describedabove, the gains G3 and G4 are determined for the charge amplifiersassociated with each electrode pair. Thereafter G1+G2 is compared withG3+G4, from which a coefficient k is deduced so that G1+G2=k(G3+G4). Thecoefficient k is then applied during demodulated detection at theresonant frequency. It should be observed that gain balancing isdescribed above with reference to two groups of electrodes in quadratureeach comprising four electrodes. It is also possible to equalize gain ontwo electrodes only, e.g. by measuring G1 on electrode 5.2 only and G3on electrode 5.1 only and then determining the coefficient k so thatG1=k G3.

[0036] Naturally, the invention is not limited to the implementationsdescribed and it may be subjected to variations that will appear to theperson skilled in the art without going beyond the ambit of theinvention as defined by the claims.

[0037] In particular, although the method of the invention is describedabove in association with an amplitude control signal at a frequencythat is twice the resonant frequency during the sustaining stage,thereby simplifying equations in rate gyro mode since the precessionsignal is itself at a frequency that is twice the resonant frequency, itis possible to apply the amplitude control signal at the resonantfrequency.

[0038] Similarly, in rate gyro mode, if it is desired to simplifycalculation by accepting a small amount of drift, it is possible toapply quadrature control at the resonant frequency or at twice theresonant frequency.

[0039] Furthermore, applying a DC quadrature signal together withamplitude control at a frequency twice the resonant frequency tends tocause dynamic range to be lost. If it is desired to recover a largedynamic range while accepting a partial deterioration in stability, itis possible to apply quadrature control as a DC signal while applyingamplitude control at the resonant frequency.

[0040] In the preferred implementation, amplitude control is applied sothat the resulting vibration presents nodes between the electrodes, thusmaking it possible to obtain large variations of airgap in register withthe electrodes and thus maximum cross-modulation between the airgapvariations and the DC control signals or the control signals at afrequency twice the resonant frequency. The method of the invention canalso be implemented with a smaller dynamic range by generating vibrationin conventional manner so that the vibration presents nodes andantinodes in register with electrodes. This loss of dynamic range thenneeds to be compensated by more powerful control electronics anddetection electronics.

[0041] Although the invention is described above with reference to ahemispherical resonator, the invention applies to any electrostaticallycontrolled resonator.

What is claimed is:
 1. A method of implementing a resonator in rate gyro mode, the resonator comprising a vibrating member adapted to be set into vibration at a resonant frequency under the effect of electrostatic forces generated by electrodes placed facing a portion of the vibrating member, the method comprising the steps of exciting the vibrating member by means of a combination of control signals comprising an amplitude control signal, a precession control signal, and an amplitude-modulated quadrature control signal, of measuring vibration of the vibrating member, and of demodulating the vibration at the resonant frequency of the vibrating member, wherein the precession control signal is applied at a frequency that is twice the resonant frequency.
 2. A method according to claim 1, wherein, during a stage of setting into vibration, the amplitude control signal is applied at the resonant frequency of the vibrating member, and during a stage of sustaining vibration, the amplitude control signal is applied at a frequency twice the resonant frequency.
 3. A method according to claim 2, wherein, during the sustaining stage, the amplitude control signal is applied to at least half of the electrodes distributed symmetrically about the vibrating member, or to the vibrating member itself.
 4. A method according to claim 1, wherein the amplitude control signal is applied in such a manner that the vibration of the vibrating member is oriented so that a vibration node is in register with each gap between two electrodes.
 5. A method according to claim 3, wherein the amplitude control signal is applied in such a manner that the vibration of the vibrating member is oriented so that a vibration node is in register with each gap between two electrodes, and wherein, at least during the stage of setting into vibration, the amplitude control signal is applied to at least two electrodes that are modally in quadrature relative to each other.
 6. A method according to claim 1, wherein the quadrature control signal is a DC signal applied to electrodes common to the amplitude control signal and to the precession control signal.
 7. A method of implementing a resonator in free gyro mode, the resonator comprising a vibrating member adapted to be set into vibration at a resonant frequency under the effect of electrostatic forces generated by electrodes disposed facing a portion of the vibrating member, the method comprising the steps of exciting the vibrating member by means of a combination of control signals comprising, during a sustaining stage, an amplitude control signal at a frequency twice the resonant frequency of the vibrating member, and a DC quadrature control signal, both control signals being amplitude-modulated, of measuring vibration of the vibrating member, and of demodulating the vibration at the resonant frequency of the vibrating member, wherein the amplitude control signals and the quadrature control signals are applied in quadrature to common electrodes.
 8. A method according to claim 7, wherein the amplitude control signal is applied to at least half of the electrodes that are distributed in symmetrical manner.
 9. A method according to claim 7, wherein the quadrature control signal is applied to electrodes on either side of a vibration node.
 10. A method of implementing a resonator in free gyro mode, the resonator comprising a vibrating member adapted to be set into vibration at a resonant frequency by means of a combination of control signals comprising, during a sustaining stage, an amplitude control signal at a frequency twice the resonant frequency of the vibrating member, and a DC quadrature control signal, both control signals being amplitude-modulated, the method including the steps of applying the amplitude control signal to the vibrating member itself, of applying the quadrature control signal to the electrodes disposed facing the vibrating member, and of simultaneously detecting vibration of the vibrating member using the same electrodes.
 11. A method according to claim 10, wherein the quadrature control signal is applied to electrodes on either side of a vibration node of the vibrating member.
 12. A method according to claim 11, wherein the quadrature control signal is applied in alternation to two groups of electrodes that are interleaved between each other.
 13. A method according to claim 10, wherein detection gain of electrodes in quadrature is balanced by analyzing the vibration at a frequency twice the resonant frequency in order to determine the real detection gains, and by calculating a balancing coefficient. 